I am trying to understand the use of Primary Partitions. When do you make a partition a "Primary Partition"?

Should /, /boot, /tmp be primary?

It does not make any difference any more
Back in the old days they kept only 2 bits in the partition table for the partition numbering. So you could have only 4 partitions. 00, 01, 10,11.

In order to overcome this and keep compatibility, they said, lets keep it this way, and use a primary partition as extended partition, and make logical partitions inside this extended partition.

SO you may have 4 primary partitions (the one should be the extended) and you may have up to 65 logical partitions (I think, not sure about the exact number), inside the extended partition. The only restriction on the logical partitions is that they must be continuous. No unallocated space between logical partitions is allowed.

Some old OS's like DOS or windows 95-98 can not boot from logical partitions, but in linux, you may use whatever partition scheme you prefer.